It’s a Small World After All.

Sun Kissed Earth

It’s a small world but we all run in big circles.

Sasha Azevedo

How many people do you know? Let’s take a round number, like 100, as a good average guess. If your 100 acquaintances each know another 100 different people then you are connected by one step to 10,000 people: you are actually better connected than you thought. After n of these steps you are connected to 102(n+1) people. As of this month the population of the world is estimated to be 6.65 billion, which is 109.8, and so when 2(n+1) is bigger than 9.8 you have more connections than the whole population of the world. This happens when n is bigger than 3.9, so just 4 steps would do it. This is a rather remarkable conclusion. It makes a lot of simple assumptions that are not quite true, like the one about all your friend’s friends being different from each other. But if you do the counting more carefully to take that into account, it doesn’t make much difference. Just six steps is enough to put you in contact with just about anyone on Earth. Try it – you will be surprised how often fewer than 6 steps links you to famous people.
There is a hidden assumption in this that is not well tested by thinking about your links to the Prime Minister, David Beckham or the Pope. You will be surprisingly close to these famous people because they have many links with others. But try linking to an Amazonian Indian tribe member or a Mongolian herdsman and you will find that the chain of links is much longer. You might not even be able to close it. These individuals live in ‘cliques’, which have very simple links once you look beyond their immediate close knit communities. If your network of connections is a chain or a circle, then you are only connected by one person on either side and overall connectedness is poor. However, if you are in a ring of these connections with some other random links added, then you can get from one point on the ring to any other very quickly.

World Map

In recent years we have begun to appreciate how dramatic the effects of a few long-range connections can be for the overall connectivity. A group of hubs that produce lots of connections to nearby places can be linked up very effectively by just adding a few long-range connections between them. These insights are important when it comes to figuring out how much coverage you need in order for mobile phone links between all users to be possible, or how a few infected individuals can spread a disease by their interactions with members of a population. When airlines try to plan how they arrange hubs and routes so as to miniseries journey times, or maximize the number of cities they can connect with a single change of planes or minimize costs, they need to understand the unexpected properties of these
‘small world’ networks.

The study of contentedness shows us that the ‘world’ exists at many levels: transport links, phone lines, email paths all create networks of interconnections that bind us together in unlikely ways. Everything is rather closer than we thought.

Also Read:- Why Does the Other Queue Always Move Faster?

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